Practice question

**Superposition principle** states resultant displacement equals algebraic sum of individual waves, y = y₁ + y₂. For coherent waves with phase difference φ, resultant amplitude A = √(a₁² + a₂² + 2a₁a₂ cosφ), equal amplitudes give A = 2a cos(φ/2), constructive when φ = 2nπ, destructive when φ = (2n+1)π. Amplitude: A = 2a cos (Φ/2) , where a = 3 m , Φ = π/2 . A = 2 × 3 cos π/4 = 6 × (1/√(2)) = 3√(2) ≈ 4.24 m . Using v = fλ and standing-wave condition fₙ = n v/(2L) or v/(4L) as applicable, calculation yields 4.2 m, illustrating frequency-length-speed interdependence and quantization by boundaries.